Nuclear Magnetic Resonance (NMR) Spectroscopy

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April 28, 2016

Exam #3:

Graded exams on Tuesday!

Final Exam

Tuesday, May 10

th

_{, 10:30 a.m.}

Room: Votey 207

(tentative)

Review Session:

Sunday, May 8

th

_{, 4 pm, Kalkin 325}

_(tentative)

Office Hours – Next week:

moved to Wednesday, May 4

th

_{, 2:00-3:30 pm}

Nuclear Magnetic

Resonance (NMR)

Spectroscopy

Chem 221

Instrumental Analysis

Spring 2016

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Overview

Based on the interaction of RF EMR (up to ~1000 MHz) with matter (in a magnetic field)

-EMR interactions with spin states of nuclei -RF EMR: much lower energy than optical EMR First demonstrated in 1946

First commercial instrument: 1956 We will be concerned with:

origin of RF EMR interactions

how these interactions are measured

how chemical information can be obtained from NMR measurements

Theory: Quantum Treatment

Energies of nuclear spin states are quantized:

Nuclear Spin Quantum Number (I) where I = 0, ½, 1, 1½, etc.

Three Groups of Nuclei: 1. I=0

-non-spinning nuclei, no magnetic moment, even # p+_{& n}o -examples: 12_C,16_O

2. I=½

-spherical spinning charge with magnetic moment -examples: 13_C,1_H

3. I>½

-non-spherical spinning charge with magnetic moment -examples: 2_H,14_N

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More Quantum Numbers

All nuclear spin states are degenerate unless in

a uniform magnetic field

Where they split into 2I + 1 states

Defined by Magnetic Quantum Numbers (m):

m = I, I-1, I-2 . . . . -I

So, for I=0: m = 0 (only 1 state) NMR inactive for I=½: m = ±½ (2 states) NMR ACTIVE

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Energy States

For an I=½ system:

E

No MagField MagField

m = -½

m = +½

∆

E = 2µ

β

B

_o

Particle magnetic moment:

2.7927 nuclear magnetons (for 1_H)

Nuclear Magneton:

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In General:

Selection Rule:

∆

m = ±1

For any value of I:

h

ν

= (µ

β

B

_o

)/I

•So, ν will vary with applied field strength (B_o) •Example: for 1_H,_ν _{= 60 MHz @ B}

o= 14,092 Gauss

A Classical

Perspective

A“classical” view will help us understand the

measurement process.

Consider a spinning charged particle in a magnetic field: •Particle will precess at a characteristic frequency (Larmor Frequency)

ν

_o:

ν

_o

=

γ

B

_o

/2

π

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“Classical” view of

Absorption

Application of another magnetic field (B₁) perpendicular

to B_o and at a frequency = ν_oresults in:

Absorption of applied EMR

Spin flip of particle to excited state

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Instrumental

Continuous Wave (CW) NMR

original instruments used:

Electromagnets (14 - 23 kG; 60 - 100 MHz) Fixed frequency RF source

Swept (variable) magnetic field -measure absorption of applied RF

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Back to Boltzmann!

Using Boltzmann statistics, we can determine the relative populations of each of the two spin states:

N

₂

/N

₁

= e

-

∆

E/kT

•∆E is very small (relative to optical EMR) for RF EMR •As ∆E ↓, N₂/N₁ →1 (so, N₂≈ N₁)

•BUT: for absorbance, we want N₁ >> N₂

•If absorption rate > decay rate, not much absorbance can occur before N₁ = N₂ (saturation)

•When transition is saturated, NO MORE ABSORPTION!

Decay (relaxation) Processes

Two decay routes (non-radiative):

1. Spin-Lattice Relaxation (T₁)

-also called: longitudinal relaxation

-due to interactions between nuclear spin states and magnetic micro environments in the sample -magnetic micro environments must be at the

Larmor Frequency of the absorbing nuclei in

order to couple

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Coupling Efficiency: T

₁

T₁is the excited state lifetime associated with spin-lattice relaxation (it is inversely proportional to the extent of spin-lattice relaxation)

Temperature effects

-at some temperature, the frequency of molecular motion matches the Larmor frequency for a nucleus and coupling efficiency is at a maximum (T₁ is at a minimum) -any change in temperature will result in an increase in T₁(decreased coupling efficiency)

Any (e.g., viscosity) changes in lattice mobility will have a similar effect

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More on T

₁

Processes

Other lattice components that can reduce T

₁

:

unpaired electrons (from radicals and paramagnetic species, like O₂)

nuclei with I ≥1

Efficient Spin-Lattice Relaxation results in:

Decreased likelihood of saturation Larger absorption signal (CW NMR) Other effects?

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Spin-Spin Relaxation: T

₂

Energy transfer with other magnetic nuclei

Nuclei must be in close proximity

Very efficient coupling in solids (T₂ ~ 10-4_sec)

Has no effect on saturation Will cause line broadening:

∆ν= (2π∆t)-1 _{(according to Heisenberg)}

so: linewidth ∝1/T₂

(T2 ≈10-4sec → ∆ν ≈103Hz)

In solutions: (<1 sec)

T

₂

<

T

₁ (1-10 sec) Controls linewidths (~1 Hz) _{Affects saturation}

How can S/N be increased?

Increase B

_o

-increases ∆E, increasing population difference between spin states, so more nuclei can undergo transitions

-How? Superconducting Magnets

Multiplex Signal Measurement

-small signal makes measurement limited by detector noise, so a multiplex measurement method should improve S/N

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Pulsed FT-NMR

At fixed B

_o

, irradiate sample with a range

of RF EMR frequencies . . . How?

-by pulsing a fixed frequency (ν_o) RF source, a range (∆ν) of RF frequencies is generated. -the extent of the range is determined by the pulse width:

∆ν

= 1/4

τ

(according to Heisenberg) where:

τ

is the pulse width (seconds)

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The Pulsed FT-NMR

Measurement

RF Excitation Pulse Free Induction Decay

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FT-NMR:

Obtaining a Spectrum

Obtain maximum number of excited nuclei during the RF pulse (saturation)

Measure RF Emission (signal generated by nuclei spin flips back to ground state) when RF source is off - FID

FID contains emission from all excited nuclei all at

their characteristic (Larmor) frequencies Use Fourier Transform to convert time domain FID to frequency domain spectrum